Recitation R3
Response to 'Muddiest Part of the Recitation Cards'
(10 respondents)
1) When do we need all the log identities in finding Big-O?
You don’t need all of the log identities at all times. You have to pick and choose the
required identity in order to solve/ simplify the recurrence equation. For example,
when you have to find the base case, you use n = 2k, then you can represent k as log2n
2) In algorithm classes, do they prove similar forms to the master method for different
recurrence equations? Is that the non-simplified master-method?
What we looked at in class is the solution to recurrence equations of the form:
T(n) = aT(n/b) + cnk
The form that you will see in algorithm classes, treats the second term in the right
hand side to be generic i.e.
T(n) = aT(n/b) + f(n)
In this case, the master theorem appears as shown below:
3) Why cannot I from example 2 be expressed in terms of N?
Example 2, uses the following code snippet
type Int_Array is array (Integer range <>) of Integer;
procedure Measure (A : Int_Array ) is
Sum : Integer := 0;
begin
for I in A'range loop
for J in 1 .. I loop –- only change to Ex 1
Sum := Sum + A(J);
end loop;
end loop;
end Measure;
The ‘I’ value in the outer loop changes in every iteration with a maximum value of n. It
cannot be expressed as a simple function in n.
4) Still muddy about coming up with T(n) equations from recurrence problems.
Specifically unclear on how to solve for O(n) w/o Master method.
When you are not using the master method, use iteration (Lecture 13 last semester) to
solve the recurrence equation. If the T(n) is a homogeneous function in n (all the terms
are functions of n), then find the most significant term to determine the Big-O. See
examples in both the Recitation 3 and Lecture 9 slides.
6) No mud, cool stuff, good lecture (6 students)